Tom D. answered • 01/06/14
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1) Complete the square for the X-component by combining X^2 & X terms
X^2 - X + Y^2 = 2
Now complete the square for X
(X-1/2)^2 -1/4 + Y^2 = 2
(X-1/2)^2 + Y^2 = 9/4
X^2 - X + Y^2 = 2
Now complete the square for X
(X-1/2)^2 -1/4 + Y^2 = 2
(X-1/2)^2 + Y^2 = 9/4
Tom D.
The 1/4 term is a byproduct of completing the square of X.
(X-1/2)^2 = X^2 - X + 1/4
In order to preserve equality when completing the square, we need to subtract out the 1/4 term which will bring us back to our original two terms (X^2 - X).
It is good practice to expand a completed square to ensure that it is equal to what you started with. The final form is
(X-1/2)^2 + (Y-0)^2 = (3/2)^2
Circle centered at (1/2,0) with radius 3/2
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01/06/14
Tom D.
When we subtract out the 1/4 from the left side, we then combine the constants on the right
(X-1/2)^2 -1/4 + Y^2 = 2 (after combining on right)...
(X-1/2)^2 + Y^2 = 2+1/4 = 9/4
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01/06/14
Chani B.
Oh ok!! Thank you!!
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01/06/14
Chani B.
01/06/14